Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Titan
|
| gptkbp:category |
gptkb:logic
gptkb:set_theory |
| gptkbp:contrastsWith |
finite set axioms
|
| gptkbp:enables |
construction of the set of natural numbers
|
| gptkbp:formalizes |
the existence of the set of natural numbers
|
| gptkbp:formedBy |
1908
|
| https://www.w3.org/2000/01/rdf-schema#label |
Axiom of Infinity
|
| gptkbp:introduced |
gptkb:Ernst_Zermelo
|
| gptkbp:notImpliedBy |
other Zermelo-Fraenkel axioms
|
| gptkbp:partOf |
gptkb:Zermelo-Fraenkel_set_theory
|
| gptkbp:relatedTo |
gptkb:Peano_axioms
gptkb:Axiom_of_Choice gptkb:Axiom_of_Foundation |
| gptkbp:requires |
development of arithmetic in set theory
|
| gptkbp:state |
the existence of an infinite set
|
| gptkbp:symbol |
∃x (∅ ∈ x ∧ ∀y (y ∈ x → y ∪ {y} ∈ x))
|
| gptkbp:usedIn |
gptkb:set_theory
gptkb:von_Neumann–Bernays–Gödel_set_theory gptkb:Peano_arithmetic gptkb:New_Foundations_set_theory |
| gptkbp:bfsParent |
gptkb:set_theory
|
| gptkbp:bfsLayer |
4
|